when I was a high school student I drew up an idea for an unlimited racer using a donor F-86.
1) Put a tricked out Griffon 57 V-12 in the fuselage facing aft with a long P-63 type propellor shaft running aft to the tail. (the F-86 was designed to be pushed through the air not puled by a propellor on the nose.) The propellor blades should be composite material, and with short blades that can avoid the problems that longer blades have with going supersonic. Maybe some blades taken from the Piaggio Avanti turboprop pusher that can cruise at 460 mph. stock!
2) Contra rotating propellor blades so as to minimize p-factor. Also eliminates having to "twist" the vertical fin, enlarge it or many other torque relatied mods.
3) put the radiators, oil coolers etc. in the nose inside the intake and where the 50 caliber guns formerly were. This eliminates scoops, ducts and other high drag items that are found on the Mustang and Yaks, etc.
4) Modify the ailerons so that they can be "drooped" to increase lift on take off and landings and convert the flaps to flaperons that move with aileron input for increased effectiveness and lower drag at high speeds.
5) Modify the gear to accept T-38 or other high speed wheels and tires and braking. I'm told that landing speeds for a T-38 at max allowable landing weight with flaps up is close to 200 mph.
6) Since it's not a taildragger, it can accept much higher takeoff and landing speeds. Why not chop a few feet off each wing? It has flaperons you know.
7) the airplane already has electric trim and someother niceties and because one could aggresively lighten and shorten the wing, maybe it would make sense to install a drag chute for landings.
a Heads up display so the pilot never has to look inside during the race. Or maybe some instruments with an "aural report." Hope I said that right.
9) Change the canopy out for something a lot smaller like on some of the P-51 racers.
That's all I can remember for now.